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A292447 Primes p such that sigma((p + 1) / 2) is a prime q. 1
3, 7, 17, 31, 127, 577, 3361, 4801, 6961, 8191, 31249, 131071, 171697, 524287, 982801, 1062881, 1104097, 1367857, 1407841, 1468897, 2705137, 3770257, 6822817, 7785457, 10941841, 14183137, 15557041, 18495361, 20749681, 25304497, 36278161, 38878561, 44575681 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A companion sequence of A249902.

Mersenne primes p = 2^k - 1 (A000668) are terms: sigma((p + 1) / 2) = sigma((2^k - 1 + 1) / 2) = sigma((2^(k - 1)) = 2^k - 1.

A subsequence of A178490. - Altug Alkan, Oct 02 2017

LINKS

Table of n, a(n) for n=1..33.

FORMULA

a(n) = 2*A249902(n) - 1. - Altug Alkan, Oct 02 2017

EXAMPLE

17 is a term because sigma((17 + 1) / 2) = sigma(9) = 13 (prime).

MATHEMATICA

Select[Prime@ Range[10^6], PrimeQ@ DivisorSigma[1, (# + 1)/2] &] (* Michael De Vlieger, Sep 16 2017 *)

PROG

(MAGMA) [n: n in [1..10^8] | IsPrime(n) and IsPrime(SumOfDivisors((n+1) div 2))]

(PARI) lista(nn) = forprime(p=3, nn, if(isprime(sigma((p+1)/2)), print1(p, ", "))); \\ Altug Alkan, Oct 02 2017

CROSSREFS

Cf. A000203, A000668, A178490, A249902, A292448.

Sequence in context: A275631 A048860 A233930 * A176690 A295089 A168582

Adjacent sequences:  A292444 A292445 A292446 * A292448 A292449 A292450

KEYWORD

nonn,easy

AUTHOR

Jaroslav Krizek, Sep 16 2017

STATUS

approved

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Last modified October 17 06:08 EDT 2019. Contains 328106 sequences. (Running on oeis4.)